Heretofore, a glass substrate have been produced by melting a glass raw material at high temperature, sufficiently stirring such a molten glass, forming the molten glass into flat plate shape, and cooling the formed glass. In the step of melting the raw material, a large number of bubbles are generated in the molten glass.
Heretofore, in order to solve this problem, mixing of refining agent, or bubbling or stirring of molten glass (refer to JP-A-2004-91307 and JP-A-11-349335) to promote moving up of bubbles to a surface and breaking bubbles on a molten glass surface to remove bubbles. However, even by using these means, there are problems such as unevenness of glass composition or bubbles remaining unbroken on a molten glass surface, particularly, there is often a problem that bubbles remaining on a surface of molten glass in a refiner are got into inside of the glass at a time of forming the glass, to form defects in a glass substrate.    Patent Document 1: JP-A-2004-91307    Patent Document 2: JP-A-11-349335